Jiro comments on The Power of Noise - LessWrong
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I asked judge Richard Posner (one of my dissertation advisers) if he would be willing to use lotteries as a judge and he said no, it would get him impeached.
The legal system is based on the legal fiction that the judge can infallibly make a decision. If the judge makes a decision in a way which is guaranteed to be fallible in a certain percentage of cases, he violates this assumption, even if the guaranteed fallibility from randomness is less than his normal fallibility when not using randomness.